Application of Edwards' statistical mechanics to high-dimensional jammed sphere packings.

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The isostatic jamming limit of frictionless spherical particles from Edwards' statistical mechanics [Song et al., Nature (London) 453, 629 (2008)] is generalized to arbitrary dimension d using a liquid-state description. The asymptotic high-dimensional behavior of the self-consistent relation is obtained by saddle-point evaluation and checked numerically. The resulting random close packing density scaling ϕ∼d2(-d) is consistent with that of other approaches, such as replica theory and density-functional theory. The validity of various structural approximations is assessed by comparing with three- to six-dimensional isostatic packings obtained from simulations. These numerical results support a growing accuracy of the theoretical approach with dimension. The approach could thus serve as a starting point to obtain a geometrical understanding of the higher-order correlations present in jammed packings.





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Jin, Yuliang, Patrick Charbonneau, Sam Meyer, Chaoming Song and Francesco Zamponi (2010). Application of Edwards' statistical mechanics to high-dimensional jammed sphere packings. Phys Rev E Stat Nonlin Soft Matter Phys, 82(5 Pt 1). p. 051126. 10.1103/PhysRevE.82.051126 Retrieved from

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Patrick Charbonneau

Professor of Chemistry

Professor Charbonneau studies soft matter. His work combines theory and simulation to understand the glass problem, protein crystallization, microphase formation, and colloidal assembly in external fields.

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